Paper Citation Record · LEDGER

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences

As of 11 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2607.04217.

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pith.paper-citation-record.v1
2607.04217 v1

Coverage vector

measured 25 of 25 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-07-11T20:53:18.229285Z

measured 25 of 25 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Reference resolution

25 of 25 outbound references displayed

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Outbound references

Observation d564056d-988e-4fd9-93b5-0ce1e27bc989 · outbound

This paper cites Aubert and B.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Aubert and B

Reference 1

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Observation 096c5968-7c1d-4fb9-8142-a5ea0918ed86 · outbound

This paper cites Bivariate Generating Functions for a Class of Linear Recurrences: General Structure.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Bivariate Generating Functions for a Class of Linear Recurrences: General Structure

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 9ea43882-5ef9-45a8-9ecf-f7f0c61e05ae · outbound

This paper cites Brenti, Log-concave and unimodal sequences in algebra, combinatorics, and geometry: an update, Contemp.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Brenti, Log-concave and unimodal sequences in algebra, combinatorics, and geometry: an update, Contemp

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 6f2af48d-9cf4-4626-a671-33161825b96e · outbound

This paper cites Recurrence Relations for Strongly q-Log-Convex Polynomials.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Recurrence Relations for Strongly q-Log-Convex Polynomials

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation d92a4ebb-46ae-4823-89cd-a61055853e34 · outbound

This paper cites Fallat and C.R.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Fallat and C.R

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 4dff003c-48da-4404-9f12-bf13aea02563 · outbound

This paper cites Fuchs,Partially Ordered Algebraic Systems(Dover Publications Inc., Mineola NY, 2011).

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Fuchs,Partially Ordered Algebraic Systems(Dover Publications Inc., Mineola NY, 2011)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 2ac38008-43b9-43ae-bbc2-413d0d848799 · outbound

This paper cites Gantmacher and M.G.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Gantmacher and M.G

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 78f671e4-453c-48d0-ac60-57dafbdf1ed2 · outbound

This paper cites Graham, D.E.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Graham, D.E

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation ffae387a-0f9c-43dd-bfbe-03e4c508fed5 · outbound

This paper cites Karlin,Total Positivity(Stanford University Press, Stanford CA, 1968).

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Karlin,Total Positivity(Stanford University Press, Stanford CA, 1968)

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation e6f151a7-9c4c-4d2c-a7bd-05cb2aa377e9 · outbound

This paper cites Kurtz, A note on concavity properties of triangular arrays of numbers, J.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Kurtz, A note on concavity properties of triangular arrays of numbers, J

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation af91a302-2e0f-48f1-9123-4f61ee3e97ce · outbound

This paper cites On the log-convexity of combinatorial sequences.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences On the log-convexity of combinatorial sequences

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 461df0f5-f174-4a9f-9640-5ea115d05919 · outbound

This paper cites Triangular Recurrences, Generalized Eulerian Numbers, and Related Number Triangles.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Triangular Recurrences, Generalized Eulerian Numbers, and Related Number Triangles

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 9253c7f5-648d-444a-80cf-276ba83395f3 · outbound

This paper cites Mansour and M.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Mansour and M

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 6d97fb45-f237-4efd-a8eb-a0c5d04c93ad · outbound

This paper cites Neuwirth, Recursively defined combinatorial functions: extending Galton’s boards, Discrete Math.132, 33–51 (2001).

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Neuwirth, Recursively defined combinatorial functions: extending Galton’s boards, Discrete Math.132, 33–51 (2001)

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 06797c20-6566-4907-a0ff-66adf5f0eaa7 · outbound

This paper cites Pinkus,Totally Positive Matrices(Cambridge University Press, Cambridge, UK, 2010).

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Pinkus,Totally Positive Matrices(Cambridge University Press, Cambridge, UK, 2010)

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 7d7ba7ef-6673-4b46-81c0-d6845998f2f7 · outbound

This paper cites The Graham--Knuth--Patashnik recurrence: Symmetries and continued fractions.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences The Graham--Knuth--Patashnik recurrence: Symmetries and continued fractions

Reference 16

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Observation 43c4318b-57ef-4666-83ee-15990761950b · outbound

This paper cites Log-concavity and strong log-concavity: a review.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Log-concavity and strong log-concavity: a review

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 3df8341c-2acc-419c-9d9c-0341b5c28132 · outbound

This paper cites Sokal, unpublished (2014).

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Sokal, unpublished (2014)

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation f7a40363-5c32-4d8f-b835-9c5487c83dc9 · outbound

This paper cites Sokal, Coefficientwise Hankel-total positivity, in preparation (2026).

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Sokal, Coefficientwise Hankel-total positivity, in preparation (2026)

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation e3dd1606-dc2d-4425-a5f2-bc07016807c7 · outbound

This paper cites Spivey, On solutions to a general combinatorial recurrence, J.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Spivey, On solutions to a general combinatorial recurrence, J

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation fda3a2dc-c830-4446-ba47-1b95ae5e7085 · outbound

This paper cites Stanley, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Ann.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Stanley, Log-concave and unimodal sequences in algebra, combinatorics, and geometry, Ann

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation f99b0008-f8e3-4c39-a3c8-3b60b97f9991 · outbound

This paper cites an unresolved cited work.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Unresolved cited work

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation 4c1f71bc-b944-403e-a111-c455cbba197e · outbound

This paper cites Th´ eorˆ et, Fonctions g´ en´ eratrices pour une classe d’´ equations aux diff´ erences partielles, Ann.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Th´ eorˆ et, Fonctions g´ en´ eratrices pour une classe d’´ equations aux diff´ erences partielles, Ann

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation c3844f95-c8db-44a2-ae4a-785b45b587f2 · outbound

This paper cites Th´ eorˆ et, Relations matricielles pour hyperbinomiales, Ann.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences Th´ eorˆ et, Relations matricielles pour hyperbinomiales, Ann

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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Observation ba0ce23c-a197-4bd7-8199-95b8f9296f45 · outbound

This paper cites The method of characteristics, and "problem 89" of Graham, Knuth and Patashnik.

Log-concavity and log-convexity in the theory of the Graham--Knuth--Patashnik recurrences The method of characteristics, and "problem 89" of Graham, Knuth and Patashnik

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-11T20:53:18.229285Z

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